Question: Simplify the following expression and state the condition under which the simplification is valid: $z = \dfrac{p^2 + 17p + 70}{p^2 + 10p}$
Solution: First factor the expressions in the numerator and denominator. $ \dfrac{p^2 + 17p + 70}{p^2 + 10p} = \dfrac{(p + 7)(p + 10)}{(p)(p + 10)} $ Notice that the term $(p + 10)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(p + 10)$ gives: $z = \dfrac{p + 7}{p}$ Since we divided by $(p + 10)$, $p \neq -10$. $z = \dfrac{p + 7}{p}; \space p \neq -10$